Wanmin Liu: On exceptional collections of line bundles of maximal length on the blow-ups of P^3
Tid: On 2017-10-04 kl 13.15 - 14.15
Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University
Medverkande: Wanmin Liu (IBS Center for Geometry and Physics)
To investigate varieties via their derived categories, Bondal and Orlov introduced the notion of semiorthogonal decomposition (SOD). In particular, SOD includes full exceptional collection as a special example. Finding a good condition for an exceptional collection to be full is hard in general. Kuznetsov proposed the following fullness conjecture: if a smooth projective variety admits a full exceptional collection (of line bundles) of length l, then any exceptional collection (of line bundles) of length l is still full.
In this talk, we will focus on three examples. Let X be the blow-up of \(\mathbb{P}^3\) at a point, or a line, or a twisted cubic curve. We show that any exceptional collection of line bundles of length 6 on X is full.
This is a joint work with Song Yang and Xun Yu. The paper is available at the IBS-CGP preprint system [CGP17025] .